Interelement Stress Evaluation by Boundary Elements

Zhao, Zhiye

doi:10.1002/(sici)1097-0207(19960730)39:14<2399::aid-nme964>3.0.co;2-3

Cited by 10 publications

(2 citation statements)

References 8 publications

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“…In order to avoid discontinuities of such derivatives at boundary element junctions and also to obtain results of a higher order of accuracy, several averaging or smoothing techniques have been proposed recently by various authors (Zhao 1996;Schwab and Wendland 1999;Mantic Ï et al 1999a, b).…”

Section: Introductionmentioning

confidence: 99%

A critical study of hypersingular and strongly singular boundary integral representations of potential gradient

Graciani

Mantič

Parı́s

et al. 2000

Computational Mechanics

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This paper deals with recovery of potential gradient (ru) in the resolution of the two-dimensional Laplace equation by boundary element method. The emphasis is placed on ru-recovery near and on the boundary, where error behaviour and convergence rate are studied in detail. Conventional hypersingular (HS) and strongly singular (SS) boundary integral representations (BIRs) of ru are compared with two recovery procedures recently introduced by Mantic Ï, Graciani and Parõ Âs, Comput. Methods Appl. Mech. Engrg (1999) 178, pp. 267±289: DSC ± a local smoothing procedure, and SSC -applying SS BIR with the integral density obtained previously from DSC. The theoretical analysis of error of ru recovered by ru-BIRs presented is supported by numerical examples. The numerical study of convergence carried out using an h-re®nement of (quasi)uniform meshes of linear boundary elements shows a slow convergence rate, Oh or less, of HS and SS BIRs in comparison with superconvergence rate Oh 2 of DSC (only on the boundary) and SSC near the boundary and at element centres and junctions between elements. A slow convergence rate is obtained by all approximations at boundary corners, SSC clearly providing the most accurate results. Superconvergent results of HS and SS BIRs are only obtained in a particular case of evaluation of tangential derivative of potential on a straight part of the boundary.

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Section: Introductionmentioning

confidence: 99%

A critical study of hypersingular and strongly singular boundary integral representations of potential gradient

Graciani

Mantič

Parı́s

et al. 2000

Computational Mechanics

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“…A survey of previous collocation algorithms for gradient evaluation, most of which is focused on surface stress, is given in [23,42,52]. Recent methods include smoothing techniques [19,37,38,53] and direct collocation methods [10,52]; a comparison of several gradient procedures is presented in [54].…”

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confidence: 99%

Boundary Integral Evaluation of Surface Derivatives

Gray¹,

Phan²,

Kaplan³

2004

SIAM J. Sci. Comput.

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In boundary element analysis, first order function derivatives, e.g., boundary potential gradient or stress tensor, can be accurately computed by evaluating the hypersingular integral equation for these quantities. However, this approach requires a complete integration over the boundary and is therefore computationally quite expensive. Herein it is shown that this method can be significantly simplified: only local singular integrals need to be evaluated. The procedure is based upon defining the singular integrals as a limit to the boundary and exploiting the ability to use both interior and exterior boundary limits. Test calculations for two-and three-dimensional problems demonstrate the accuracy of the method.

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Use of the tangent derivative boundary integral equations for the efficient computation of stresses and error indicators

Muci-Küchler

Miranda-Valenzuela

Soriano-Soriano³

2001

Numerical Meth Engineering

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SUMMARYIn this work, a new global reanalysis technique for the e cient computation of stresses and error indicators in two-dimensional elastostatic problems is presented. In the context of the boundary element method, the global reanalysis technique can be viewed as a post-processing activity that is carried out once an analysis using Lagrangian elements has been performed. To do the reanalysis, the functional representation for the displacements is changed from Lagrangian to Hermite, introducing the nodal values of the tangential derivatives of those quantities as additional degrees of freedom. Next, assuming that the nodal values of the displacements and the tractions remain practically unchanged from the ones obtained in the analysis using Lagrangian elements, the tangent derivative boundary integral equations are collocated at each functional node in order to determine the additional degrees of freedom that were introduced. Under this scheme, a second system of equations is generated and, once it is solved, the nodal values of the tangential derivatives of the displacements are obtained. This approach gives more accurate results for the stresses at the nodes since it avoids the need to di erentiate the shape functions in order to obtain the normal strain in the tangential direction. When compared with the use of Hermite elements, the global reanalysis technique has the attraction that the user does not have to give as input data the additional information required by this type of elements. Another important feature of the proposed approach is that an e cient error indicator for the values of the stresses can also be obtained comparing the values for the stresses obtained through the use of Lagrangian elements and the global reanalysis technique.

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Interelement Stress Evaluation by Boundary Elements

Cited by 10 publications

References 8 publications

A critical study of hypersingular and strongly singular boundary integral representations of potential gradient

A critical study of hypersingular and strongly singular boundary integral representations of potential gradient

Boundary Integral Evaluation of Surface Derivatives

Use of the tangent derivative boundary integral equations for the efficient computation of stresses and error indicators

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